Abstract The interaction of the foundation of structures for heterogeneous soils involves the analysis of an interactive procedure of evaluating stresses and strains relationship. The stress and strains developed because of the forces induced into the soil are complex during their analysis. This is due to the mutual effect experienced between the foundation structure and the soil. The interaction of the foundation of building structures with heterogeneous soils is analyzed using the numerical modeling, charts, and programs for mechanics. An example of the numerical modeling approach used is the 3D-Nonlinear Finite Element Analysis (Ritz & Young 2009). The forces exerted by the structures and soil settlement in this paper are addressed fully, and their numerical computation is evaluated. The paper also includes the parameters such as phases involved in the construction process, the order of loading, building ratios, soil failures and proportions in thickness of soil. Introduction The interaction between the foundation structures and the heterogeneous soils is complex. Complexity comes, as a result of the loads exerted by the structures cannot only be considered the soil layers and the foundation but also the foundation structures and the superstructures(Ahmed, 2015). Soil distortion influences the stress and strain distribution between the interaction of the foundation structure and the superstructure. The analysis, therefore, involves the interaction of the foundation structures and the heterogeneous soils. The underground soil is heterogeneous that is the soil layers have varying characteristics that need to examine for quality assessment of the building structures. The foundation structures are constructed deep in the soil affecting the interaction between the structure and soil layers and the foundation with the superstructures. The analysis of the foundation structures aides in determining the responses in the soil behaviors and the structures. Before construction of the foundation structure, reliable advanced computational analysis capable of simulating the non-linear soil characteristics and the relationship between the soil layers and the foundation is carried out. Numerical models, charts, and the mechanical programs are presented in this paper precisely to analyze, design, and construct the foundation system (Santos, 2008). The uniform vertical loading of the foundation system in the subsoil with its associated soil settlement, bending moment are key factors in the construction of the structures. Their analysis involves advance formulations and calculations to estimate the magnitude and the effects it will have on the soil layers. It also helps in determining the force distribution and the consequential effects on the soil behaviors. The methods involved in the analysis should take into consideration the construction phases, soil failure, the building ratios, and the stress-strain distribution within the foundation structures and the soil layers. The paper presents the parametric study of the foundation structures design. They include the length and space of the pile, a number of piles, thickness of the raft, pile-soil and raft-soil stiffness and the pile-raft relationship. The analysis of the aforementioned parameters leads to an estimation of correct soil settlement and accurate approximation of raft bending moments and loads exerted by the piles (Bivand et.al 2008). The pile raft foundations determine the stiffness of the foundation. Therefore careful consideration is paid to the pile raft elements. The analysis is simplified by considering the vertical loading of the foundation systems with its associated interaction effects. Numerical methods employed in the analysis include Finite Element Method, Boundary Element Method, and hybrid method (Ahmed, 2015). The finite element method is used to analyze complex structures or geometry simplifying them as far as possible (Bivand et.al 2008). It further discretizes the structure for the efficient study of various parameters used in its evaluation. The dynamic analysis involving the soil-foundation-structure interaction relationships play mutual interdependence by considering the structural behavior of the soil in 3D non-linear and interface boundaries. The interaction of the foundation structures with the soil survey design also takes into consideration of the role played by the superstructures (Ahmed, 2015). The factors considered include its loading and the bending moment of the elements within the foundation system that are examined using the finite element approach (Bivand et.al 2008). The paper presents factors influencing the foundation structure-soil relationship that include construction phases, soil failure modes of soil field, building ratios, load distribution on both the foundation system and the soil (Ahmed, 2015). Numerical methods employed while analyzing the interaction of the foundation structures and the soil are discussed in details. The finite element method, building element method and the hybrid method are examples of the numerical methods applied in the analysis of the foundation system in civil engineering. The methods are helpful since they reduce the complexity involved during the analysis process. The soil layers below the foundation system influence the soil field response. The mode of loading in the foundation structure influences the deflection and force distribution within the superstructure elements in the soil-foundation interaction evaluation. The interaction of the foundation structure with the heterogeneous is best understood by considering the following methods. 1.1 Direct Method This method involves the relationship between the concepts of inertia and kinematics. The interaction of the two concepts is approximated by modeling soil and foundation structure (Ahmed, 2015). The vibrations from the soil mass supporting the foundation structures lead to kinematic interactions and the induced vibrations within the structure by the vibrations reaching the base of the foundation structure cause inertial interactions. The following equation is used in the evaluation of the combined response of inertial and kinematic interactions Where M, C, and K are the mass, damping and stiffness matrices of the whole system including both the soil and foundation structure. 1.2 Substructure Method The interaction of foundation structure and the heterogeneous soil analysis involving dividing the steps involved. The final response is evaluated by adding together the response of individual steps by the principal of superposition. Unlike in the direct method, the inertial and kinematic interactions are evaluated independently and later superimpose to obtain the response of the system. The equation above in the direct method now takes into consideration of the inertial interactions and the kinematic interactions. The final equation then will contain both the inertial and kinematic interactions equation. 1.3 Analytical Method Numerical method used in the analysis of the interaction between the foundation structures and the soil are commonly used. This is because of the easy approach and simple criteria they use while analyzing the relationship. Three methods used include; finite element method, boundary element method and the hybrid method (Ahmed, 2015). The approaches used by these methods in establishing the interaction between foundation structures and the soil behaviors is discussed in details in the following sections. The numerical analysis methods involved include both the old and the current ones that have made it easier in the analyzing the interactions. They include the following: 1.3.1 Winkler Approach Winkler approach method is referred to as sub grade reaction theory (Dean, 2010). This is one of the ancient methods used to determine the bending moments and deflections in the pile. Series of springs represents the soil whose spring constant is equivalent to the soil subgrade reaction. The results can be evaluated theoretically or by use of experiments (Dean, 2010). Standard charts are available that can be used to predict the deflections and bending moments of pile subjected to both static and dynamic loading. The limitation of the Winkler approach is that the approximation of the spring constant depends on the pile behaviors and size of deflection. The response, therefore, calculated is not realistic. 1.3.2 p-y Method This is an improvement of the Winkler approach applied in the evaluation of the horizontally loaded piles (Ahmed, 2015). In the p-y method, p represents the soil pressure while y represents the deflection of the pile. In this method, the soil model is obtained by evaluating bending equations to get non-linear load against deflection curves. The p-y curves represent the soil and these curves changes with the soli type and depth (Miller et.al 2010). 1.3.3 Elastic Continuum Approach This method is applicable where the soil is homogeneous. Therefore, it cannot be used in the analysis of the interaction between the foundation structures and heterogeneous soil. The method is used to analyze the characteristics of the laterally loaded piles. The assumption made in the elastic continuum approach is that the piles are rectangular vertical strips. The strip elements are under the influence of horizontal forces. In the elastic continuum method, the size of the load, the height of overhang of the pile, pile, and soil stiffness are factors that determine the load-displacement characteristics of the foundation system. 1.3.4 Finite Element Method (FEM) The finite element method applies the concept of the continuum approach. The method is used in the numerical analysis of the complex geometry of foundation systems. In this approach, the system is discretized into finite elements whose loading characteristics can then be analyzed. The advantage of the finite element method can be used in the analysis of large-scale model. The soil is modeled as a continuum and numerical methods like Galerkin, Rayleigh is applied to solve for individual finite properties (Dean, 2010). The soil non-linearity in this approach is converted to linear form and simulations are possible by use of programs like MATLAB. The stresses, strain, and deflections of the pile are analyzed by the help of beam bending equation to represent structural elements and soil interactions (Hicks, 2007). Conclusion The numerical methods applied in the analysis of the soil- foundation structure interaction are very efficient. The methods can be used to analyze even complex structures and make decisive recommendations. Finite element method and boundary element method are combined together for easier analysis of the interaction of structures and the soil. FEM is only discretizing the whole system into finite elements whose behavioral properties are then determined. REFERENCES Ahmed, M. (2015). Soil-Foundation-Structure Interaction analysis using Finite Elements. Saarbru??cken: LAP LAMBERT Academic Publishing. Bivand, R., Pebesma, E. & Rubio, V. (2008). Applied spatial data analysis with R. 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